Continuous Charge Distribution

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge $Q$. A charge $q$ is placed at the centre of the shell.
What is the surface charge density on the (i) inner surface, (ii) outer surface of the shell?

Two isolated hollow spheres of radius $2R$ and $R$ are charged to $V$ volts and $\frac{V}{2}$ volts respectively. Now the smaller sphere is inserted into the bigger sphere such that net charge on each sphere reamin same, then the potential difference between the two spheres becomes $\frac{V}{n}$. Find $n$.

Describe linear charge density. Write its SI unit.

What is volume charge distribution?

There is a conducting shell of inner radius $8 \mathrm{cm}$ and outer radius $10 \mathrm{cm}.$ Inside this shell, there is a charge of $(+5\mu \mathrm{C})$ at a distance of $5 \mathrm{cm}$ from the centre of the shell, then the force experienced by a charge $(+10\mu \mathrm{C})$ at $a$ distance $12 \mathrm{cm}$ from the centre is $\left(k=\frac{1}{4\pi {\epsilon }_0}\right)$

Two conducting spheres of radii $r_1$ and $r_2$ have equal surface charge densities. The ratio of their charges is ___.

Explain the term volume charge density. Write its SI unit.

Explain the term surface charge density. Write its Sl unit.

Find the total charge on a thin disc of radius $R$, if its surface charge density varies with distance $r$ from centre as $\sigma ={\sigma }_0\frac{R}{r}$. 

What will be the potential difference between two points $\mathrm{A}$ and $\mathrm{B}$ in front of an infinitely long line of charge of linear charge density $\lambda$, as shown in figure ?

A straight infinitely long cylinder of radius ${\mathrm{R}}_0=10\mathrm{c}\mathrm{m}$ is uniformly charged with a surface charge density $\mathrm{\sigma }=+{10}^{–12}\mathrm{C}/{\mathrm{m}}^2$. The cylinder serves as a source of electrons, with the velocity of the emitted electrons perpendicular to its surface. Electron velocity must be $\dots \times {10}^5\mathrm{m}/\mathrm{s}$ to ensure that electrons can move away, from the axis of the cylinder to a distance greater than $\mathrm{r}={10}^3\mathrm{m}$.

Two metal spheres, one of radius $R$ and the other of radius $2R$ , both have same surface charge density $\sigma$ . If they are brought in contact and separated, then the new surface charge density on each of the sphere are respectively

The surface density of charge on the surface of a charged conductor in the air is $26.5 \mathrm{\mu }\mathrm{C} {\mathrm{m}}^{-2}$. Then the outward force per unit area of the charged conductor is $\left({\mathrm{\epsilon }}_0=8.85\times {10}^{-12} {\mathrm{C}}^2 {\mathrm{N}}^{-1} {\mathrm{m}}^{-2}\right)$

An infinite long line charge of charge per unit length $\lambda$ is passing one of the edge of a cube. Length of edge of the cube is $l$. (see figure)

The figure shows two large, closely placed, parallel, nonconducting sheets with identical (positive) uniform surface charge densities, and a sphere with a uniform (positive) volume charge density. Four points marked as 1, 2, 3 and 4 are shown in the space in between. If $E_1, E_2, E_3 and E_4$ are magnitude of net electric fields at these points respectively then:

A solid sphere of radius $R_1$ and volume charge density $\mathrm{\rho }=\frac{{\mathrm{\rho }}_0}{\mathrm{r}}$ is enclosed by a hollow sphere of radius ${\mathrm{R}}_2$ with negative surface charge density $\mathrm{\sigma }$ , such that the total charge in the system is zero, ${\mathrm{\rho }}_0$ is a positive constant and r is the distance from the centre of the sphere. The ratio $\frac{{\mathrm{R}}_2}{{\mathrm{R}}_1}$ is 

When a charge of amount $Q$ is given to an isolated metal plate $\mathrm{X}$ of surface area $A$, its surface charge density becomes ${\sigma }_1$. When an isolated identical plate $\mathrm{Y}$ is brought closer to $\mathrm{X}$, the surface charge density on $\mathrm{X}$ becomes ${\sigma }_2$. When $\mathrm{Y}$ is earthed, the surface charge density becomes ${\mathrm{\sigma }}_3$. Then -

Two mutually perpendicular infinitely long lines of charge having charge per unit length as ${\mathit{\text{λ}}}_1$ and ${\mathit{\text{λ}}}_2$ are located in air at a distance $a$ from each other. The force of interaction between them is

A thin glass rod is bent into a semicircle of radius $r$. A charge $+Q$ is uniformly distributed along the upper half and a charge $-Q$ is uniformly distributed along the lower half, as show in diagram. The electric field $E$ at $P$, the centre of the semicircle, is

A solid sphere of radius $R_1$ and volume charge density $\rho =\frac{{\rho }_0}{r}$ is enclosed by a hollow sphere of radius $R_2$ with negative surface charge density $\sigma$, such that the total charge in the system is zero,${\rho }_0$ is a positive constant and $r$ is the distance from the centre of sphere. The ratio $\frac{R_2}{R_1}$ is